SOLUTION: Find the equation of the tangent line to the given curves. 1. y=(7x-6)^1/3 that is perpendicular to the line 12x+7y+2=0

Question 1136445: Find the equation of the tangent line to the given curves.
1. y=(7x-6)^1/3 that is perpendicular to the line 12x+7y+2=0
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The slope of the given line is -12/7; the slope of a line perpendicular to it has a slope of 7/12.

The given curve is

The derivative is

We need to find the value of x for which the derivative (slope) is 7/12:

We need to determine the y value of the curve at x=2:

We want the equation of the line with slope 7/12 passing through (2,2):

The equation of our tangent line is

A graph....

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